During the necessary
Hermitization of \(H\) 
the main technical task is
the
construction
of the correct physical metric operator
\(\Theta \)  which would be compatible with
the Hamiltonian
crypto-Hermiticity
alias  pseudo-Hermiticity [1]}
alias  quasi-Hermiticity [2]}
condition (REF ).
It is worth a comment that the
key role of
operator \(\Theta \) 
(with the upper-case Greek-letter symbol proposed in [3]})
is in a sharp contrast
with a lack of
its sufficiently widely accepted denotation. In
Refs. [4]}, [2]} or [1]}, for example,
these
physical Hilbert-space metrics may be found denoted
by the very different symbols like \(F\) , \(T\)  or \(\eta _+\) ,
respectively.
